Math Problem Statement

The sum of three consecutive numbers is 72. What are the three numbers?

Solution

The problem states:

"The sum of three consecutive numbers is 72. What are the three numbers?"

Let's solve this step by step.

Step 1: Define the three consecutive numbers

Let the three consecutive numbers be:

  • xx (the first number),
  • x+1x + 1 (the second number),
  • x+2x + 2 (the third number).

Step 2: Set up the equation

The sum of these three numbers is given as 72: x+(x+1)+(x+2)=72x + (x + 1) + (x + 2) = 72

Step 3: Simplify the equation

Combine the like terms: 3x+3=723x + 3 = 72

Step 4: Solve for xx

Subtract 3 from both sides: 3x=693x = 69 Now, divide both sides by 3: x=23x = 23

Step 5: Find the three consecutive numbers

If x=23x = 23, then the three consecutive numbers are:

  • First number: x=23x = 23
  • Second number: x+1=24x + 1 = 24
  • Third number: x+2=25x + 2 = 25

So, the three consecutive numbers are 23, 24, and 25.

Would you like further details or explanations?

Here are five related questions that you might find helpful:

  1. What would the three consecutive numbers be if their sum was 90?
  2. How would the problem change if the numbers were consecutive even numbers?
  3. What is the sum of four consecutive numbers if the smallest number is 10?
  4. How do you set up an equation for the sum of consecutive odd numbers?
  5. What is the product of three consecutive numbers if their sum is 72?

Tip: When dealing with consecutive numbers in algebra, always express them in terms of a single variable and its increments to simplify the problem.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Sum of consecutive numbers formula: x + (x + 1) + (x + 2) = Sum

Theorems

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Suitable Grade Level

Grades 6-8